This video showing how to remove dog urine smells from carpet has some great suggestions. The first and foremost step is to get the dog urine out as soon as possible. If you are finding dog urine spots in your carpet while they are still wet you have a much better chance at getting it out then if it has already dried. The key is to act fast and absorb as much as possible. I remove dog urine smells from carpet professionally in Tampa FL and I know you can get most of the urine out of the carpet if you act quickly.
To get the dog urine smell out of the carpet place a towel on the spot and stand on it for 30 seconds. Now fold the towel over and do it again. Now take a new towel and do it again. Keep a fresh towel on the spot and stand on it for 30 seconds at a time. Do this until there is no more transfer to the towel. Yes, you can use paper towels instead.
Next take some baking soda and sprinkle it over the area, then let it sit for 24 hours. After it has sat for an entire day you can vacuum up the baking soda and move on about your life. If you vacuum up the baking soda to early you will not remove the associated odor.
If you need to remove dog urine smells after the spot has dried you will have to soak the spot with a cleaning solution and then remove it just like a normal wet urine spot. Mix a solution of 50% water and 50% vinegar in a gallon jug. Now pour this water vinegar solution over the dried dog urine spot. Use about twice as much solution as there is urine in the carpet. Let it sit in the carpet for 5 minutes to break down the urine crystals. Now remove it like a wet dog urine spot. Use several towels and be patient. The more you can remove the better it will be. Persistence is the key. If your are still having trouble with dog urine smells in your home it's time to call a professional carpet cleaner.